Herbicide to use
We do not make recommendations for one product over another, but any broad-leaf herbicide that lists your weeds on the label should be effective if the weeds are in your lawn. Because broad-leaf herbicides will also kill your desirable plants, be careful you do not spray or sprinkle the herbicide on them. Carefully follow all instructions on the label.
Hairy bittercress is one of the most difficult weeds to eradicate. Your goal is to get them before they begin to set seed. The link below will give you some help in controlling this nasty weed:
And for chickweed: